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Hereditary species as monoidal decomposition spaces, comodule bialgebras, and operadic categories

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arxiv 1903.07964 v1 pith:AMQ67TYJ submitted 2019-03-19 math.CO math.ATmath.CT

Louis Carlier This is my paper · ORCID
classification math.COmath.ATmath.CT
keywords bialgebradecompositionhereditarymonoidalspeciescategoriescomoduleconstruction
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We show that Schmitt's hereditary species induce monoidal decomposition spaces, and exhibit Schmitt's bialgebra construction as an instance of the general bialgebra construction on a monoidal decomposition space. We show furthermore that this bialgebra structure coacts on the underlying restriction-species bialgebra structure so as to form a comodule bialgebra. Finally, we show that hereditary species induce a new family of examples of operadic categories in the sense of Batanin and Markl.

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Cited by 1 Pith paper

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  1. Pita factorisation in operadic categories

    math.CT 2025-12 conditional novelty 6.0 of 10

    For strictly factorisable operadic categories, the pita nerve is a coherent top-lax simplicial category, and a decomposition space when all quasibijections are invertible.

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